Question

The greatest integer which divides $2001\times 2002\times 2003\times .......\times 2009$ is

• A. $5040$
• B. $40320$
• C. $362880$
• D. $36288$

Answer 1

Answer: (C)

$362880$

2001 x 2002 x 2003 ....... x2009

Multiply and divide by (2000)!, We get

$\frac{\left(2000\right)!\times 2001\times 2002\times ......\times 2009}{\left(2000\right)!}$

= ${}^{2009}{P}_{2000}$

= ${}^{2009}{P}_9$

and ${}^n{P}_r$ is always divisible by r!

So it is divisible by 9! = 362880